INTRODUCTION TO COMSOL Multiphysics

Transcription

1 INTRODUCTION TO COMSOL Multiphysics

2 Introduction to COMSOL Multiphysics COMSOL Protected by U.S. Patents listed on and U.S. Patents 7,519,518; 7,596,474; 7,623,991; 8,457,932; 8,954,302; 9,098,106; and 9,146,652. Patents pending. This Documentation and the Programs described herein are furnished under the COMSOL Software License Agreement ( and may be used or copied only under the terms of the license agreement. COMSOL, COMSOL Multiphysics, Capture the Concept, COMSOL Desktop, LiveLink, and COMSOL Server are either registered trademarks or trademarks of COMSOL AB. All other trademarks are the property of their respective owners, and COMSOL AB and its subsidiaries and products are not affiliated with, endorsed by, sponsored by, or supported by those trademark owners. For a list of such trademark owners, see Version: COMSOL 5.2 Contact Information Visit the Contact COMSOL page at to submit general inquiries, contact Technical Support, or search for an address and phone number. You can also visit the Worldwide Sales Offices page at for address and contact information. If you need to contact Support, an online request form is located at the COMSOL Access page at Other useful links include: Support Center: Product Download: Product Updates: COMSOL Blog: Discussion Forum: Events: COMSOL Video Gallery: Support Knowledge Base: Part number: CM010004

3 Contents Introduction COMSOL Desktop Example 1: Structural Analysis of a Wrench Example 2: The Busbar A Multiphysics Model Advanced Topics Parameters, Functions, Variables and Couplings Material Properties and Material Libraries Adding Meshes Adding Physics Parametric Sweeps Parallel Computing Appendix A Building a Geometry Appendix B Keyboard and Mouse Shortcuts Appendix C Language Elements and Reserved Names Appendix D File Formats Appendix E Connecting with LiveLink Add-Ons Contents 3

4 4 Contents

5 Introduction Read this book if you are new to COMSOL Multiphysics. It provides an overview of the COMSOL environment with examples that show you how to use the COMSOL Desktop user interface and the Model Builder. It also provides a quick introduction to creating applications using the Application Builder. If you have not yet installed the software, install it now according to the instructions at In addition to this book, an extensive documentation set is available after installation. Tutorials can be found throughout the COMSOL website, including in the Video Gallery at and in the COMSOL Blog at 5

6 COMSOL Desktop QUICK ACCESS TOOLBAR Use these buttons for access to functionality such as file open/save, undo/redo, copy/paste, and delete. RIBBON The ribbon tabs have buttons and drop-down lists for controlling all steps of the modeling process. APPLICATION BUILDER Click this button to switch to the Application Builder and start building an application based on your model. MODEL BUILDER TOOLBAR MODEL TREE The model tree gives an overview of the model and all the functionality and operations needed for building and solving a model as well as processing the results. MODEL BUILDER The Model Builder window with its model tree and the associated toolbar buttons gives you an overview of the model. The modeling process can be controlled from context-sensitive menus accessed by right-clicking a node. SETTINGS WINDOW Click any node in the model tree to see its associated Settings window displayed next to the Model Builder. 6

7 GRAPHICS WINDOW TOOLBAR GRAPHICS WINDOW The Graphics window presents interactive graphics for the Geometry, Mesh, and Results nodes. Operations include rotating, panning, zooming, and selecting. INFORMATION W1NDOWS The Information windows will display vital model information during the simulation, such as the solution time, solution progress, mesh statistics, solver logs, and, when available, results tables. 7

8 The screenshot on the previous pages is what you will see when you first start modeling in COMSOL Multiphysics using the Model Builder. COMSOL Desktop provides a complete and integrated environment for physics modeling and simulation as well as application design, providing you with the tools necessary to build a user-friendly interface for your models. You can customize the desktop to your own needs. The windows can be resized, moved, docked, and detached. Any changes you make to the layout will be saved when you close the session and available again the next time you open COMSOL Multiphysics. As you build your model, additional windows and widgets will be added. (See page 24 for an example of a more developed desktop.) Among the available windows and user interface components are the following: Quick Access Toolbar The Quick Access Toolbar gives access to functionality such as Open, Save, Undo, Redo, Copy, Paste, and Delete. You can customize its content from the Customize Quick Access Toolbar list. Ribbon The ribbon at the top of the desktop gives access to commands used to complete most modeling tasks. The ribbon is only available in the Windows version of the COMSOL Desktop environment and is replaced by menus and toolbars in the OS X and Linux versions. Click the Application Builder button to switch from the Model Builder to the Application Builder and start building an application based on your model. Settings Window This is the main window for entering all of the specifications of the model including the dimensions of the geometry, properties of the materials, boundary conditions and initial conditions, and any other information that the solver will 8

9 need to carry out the simulation. The picture below shows the Settings window for the Geometry node. Plot Windows These are the windows for graphical output. In addition to the Graphics window, Plot windows are used for visualizing results. Several Plot windows can be used to show multiple results simultaneously. A special case is the Convergence Plot window, an automatically generated Plot window that displays a graphical indication of the convergence of the solution process while a model is running. Information Windows These are the windows for non-graphical information. They include: Messages: Various information about the current COMSOL session is displayed in this window. Progress: Progress information from the solver in addition to stop buttons. Log: Information from the solver such as number of degrees of freedom, solution time, and solver iteration data. 9

10 Table: Numerical data in table format as defined in the Results branch. External Process: Provides a control panel for cluster, cloud, and batch jobs. Other Windows Add Material and the Material Browser: Access the material property libraries. The Material Browser enables editing of material properties. Selection List: A list of geometry objects, domains, boundaries, edges, and points that are currently available for selection. The Windows drop-down list in the Home tab of the ribbon gives you access to all COMSOL Desktop windows. (On OS X and Linux, you will find this in the Windows menu.) Progress Bar with Cancel Button The Progress Bar with a button for canceling the current computation, if any, is located in the lower right-hand corner of the COMSOL Desktop interface. Dynamic Help The Help window provides context-dependent help texts about windows and model tree nodes. If you have the Help window open in your desktop (by typing F1, for example), you will get dynamic help (in English only) when you click a node or a window. From the Help window you can search for other topics such as menu items. The Model Builder and the Application Builder The two main components of the COMSOL Desktop environment are the Model Builder and the Application Builder. The Model Builder is the tool where you define the model and its components: how to solve it, the analysis of results, and the reports. You do that by building a model tree. The model tree reflects the underlying data structure, the model object, which stores the state of the model including settings for: geometry, mesh, physics, boundary conditions, studies, solvers, postprocessing, and visualizations. The Application Builder allows you to quickly create an application with a specialized user interface that is easy to use. An application is based on a model created with the Model Builder. The Application Builder provides two important tools for creating applications: The Form editor and the Method editor. In addition, an application can have a menu bar or a ribbon. The Form editor includes drag-and-drop capabilities for easily accessing and including user 10

11 interface components such as input fields, graphics windows, and buttons. The Method editor is a programming environment that allows you to modify the model represented by the model object data structure. This book, Introduction to COMSOL Multiphysics, gives a detailed introduction to using the Model Builder and a quick introduction to the Application Builder. For detailed information on how to use the Application Builder, see Introduction to Application Builder. Running Applications and COMSOL Server The Application Builder is included in the Windows version of COMSOL Multiphysics. With a COMSOL Multiphysics license, applications can be run from the COMSOL Desktop. With a COMSOL Server license, applications can be run in major web browsers on a variety of operating systems and hardware platforms. In addition, you can run applications by connecting to COMSOL Server with an easy-to-install COMSOL Client for Windows. The COMSOL Client for Windows allows a user to run applications that require a LiveLink product for CAD. Running applications in a web browser does not require any installation and no web browser plug-ins are needed. Running an application in a web browser supports interactive graphics in 1D, 2D, and 3D. In a web browser, graphics rendering in 3D is based on WebGL technology which comes included with all major web browsers. To create an application based on your model, use the Application Builder, accessible from the Home tab in the ribbon. For more information on creating a COMSOL application, refer to the section Creating an Application using the New Form Wizard on page 82 and the book Introduction to Application Builder. 11

12 Preferences Preferences are settings that affect the modeling environment. Most are persistent between modeling sessions, but some are saved with the model. You access Preferences from the File menu. In the Preferences window, you can change settings such as graphics rendering, number of displayed digits for results, maximum number of CPU cores used for computations, or paths to user-defined application libraries. Take a moment to browse your current settings to familiarize yourself with the different options. There are three graphics rendering options available: OpenGL, DirectX, and Software Rendering. DirectX is not available in OS X or Linux, but is available in Windows if you choose to install the DirectX runtime libraries during installation. If your computer does not have a dedicated graphics card, you may have to switch to Software Rendering for slower but fully functional graphics. A list of recommended graphics cards can be found at: 12

13 Creating a New Model You can set up a model guided by the Model Wizard or start from a Blank Model as shown in the figure below. CREATING A MODEL GUIDED BY THE MODEL WIZARD The Model Wizard will guide you in setting up the space dimension, physics, and study type in a few steps: 1 Start by selecting the space dimension for your model component: 3D, 2D Axisymmetric, 2D, 1D Axisymmetric, or 0D. 2 Now, add one or more physics interfaces. These are organized in a number of Physics branches in order to make them easy to locate. These branches do not directly correspond to products. When products are added to your COMSOL 13

14 Multiphysics installation, one or more branches will be populated with additional physics interfaces. 14

15 3 Select the Study type that represents the solver or set of solvers that will be used for the computation. Finally, click Done. The desktop is now displayed with the model tree configured according to the choices you made in the Model Wizard. CREATING A BLANK MODEL The Blank Model option will open the COMSOL Desktop interface without any Component or Study. You can right-click the model tree to add a Component of a certain space dimension, a physics interface, or a Study. The Ribbon and Quick Access Toolbar The ribbon tabs in the COMSOL Desktop environment reflect the modeling workflow and give an overview of the functionality available for each modeling step, including building simulation applications from your models. The Home tab contains buttons for the most common operations for making changes to a model, running simulations, and for building and testing applications. Examples include changing model parameters for a parameterized 15

16 geometry, reviewing material properties and physics, building the mesh, running a study, and visualizing the simulation results. There are standard tabs for each of the main steps in the modeling process. These are ordered from left to right according to the workflow: Definitions, Geometry, Materials, Physics, Mesh, Study, and Results. Contextual tabs are shown only if and when they are needed, such as the 3D Plot Group tab, which is shown when the corresponding plot group is added or when the node is selected in the model tree. Modal tabs are used for very specific operations, when other operations in the ribbon may become temporarily irrelevant. An example is the Work Plane modal tab. When working with Work Planes, other tabs are not shown since they do not present relevant operations. THE RIBBON VS. THE MODEL BUILDER The ribbon gives quick access to available commands and complements the model tree in the Model Builder window. Most of the functionality accessed from the ribbon is also accessible from contextual menus by right-clicking nodes in the model tree. Certain operations are only available from the ribbon, such as selecting which desktop window to display. In the COMSOL Desktop interface for OS X and Linux, this functionality is available from toolbars, which replace the ribbon on these platforms. There are also operations that are only available from the model tree, such as reordering and disabling nodes. THE QUICK ACCESS TOOLBAR The Quick Access Toolbar contains a set of commands that are independent of the ribbon tab that is currently displayed. You can customize the Quick Access Toolbar; you can add most commands available in the File menu, commands for undoing and redoing recent actions, for copying, pasting, duplicating, and deleting nodes in the model tree. You can also choose to position the Quick Access Toolbar above or below the ribbon. 16

17 OS X AND LINUX In the COMSOL Desktop environment for OS X and Linux, the ribbon is replaced by a set of menus and toolbars: The instructions in this book are based on the Windows version of the COMSOL Desktop environment. However, running COMSOL in OS X and Linux is very similar, keeping in mind that ribbon user interface components can instead be found in the corresponding menus and toolbars. The Model Builder and the Model Tree Using the Model Builder, you build a model by starting with the default model tree, adding nodes, and editing the node settings. All of the nodes in the default model tree are top-level parent nodes. You can right-click on them to see a list of child nodes, or subnodes, that you can add beneath them. This is the means by which nodes are added to the tree. When you click on a child node, then you will see its node settings in the Settings window. It is here that you can edit node settings. It is worth noting that if you have the Help window open (which is achieved either by selecting Help from the File menu, or by pressing the function key F1), then you will also get dynamic help (in English only) when you click on a node. THE ROOT, GLOBAL DEFINITIONS, AND RESULTS NODES A model tree always has a root node (initially labeled Untitled.mph), a Global Definitions node, and a Results node. The label on the root node is the name of the multiphysics model file, or MPH file, that this model is saved to. The root node has settings for author name, default unit system, and more. The Global Definitions node has a Materials subnode by default. The Global Definitions node is where you define parameters, variables, functions, and couplings that can be used throughout the model tree. They can be used, for example, to define the values and functional dependencies of material properties, forces, geometry, and other relevant features. The Global Definitions node itself has no settings, but its child nodes have plenty of them. The 17

18 Global Definitions>Materials node stores material properties that can be referenced in the Component nodes of a model. The Results node is where you access the solution after performing a simulation and where you find tools for processing the data. The Results node initially has five subnodes: Data Sets, which contain a list of solutions you can work with. Derived Values, which defines values to be derived from the solution using a number of postprocessing tools. Tables, which is a convenient destination for the Derived Values or for Results generated by probes that monitor the solution in real-time while the simulation is running. Export, which defines numerical data, images, and animations to be exported to files. Reports, which contains automatically generated or custom reports about the model in HTML or Microsoft Word format. To these five default subnodes, you may also add more Plot Group subnodes that define graphs to be displayed in the Graphics window or in Plot windows. Some of these may be created automatically, depending on the type of simulations you are performing, but you may include additional figures by right-clicking on the Results node and choosing from the list of plot types. THE COMPONENT AND STUDY NODES In addition to the three nodes just described, there are two additional top-level node types: Component nodes and Study nodes. These are usually created by the Model Wizard when you create a new model. After using the Model Wizard to specify what type of physics you are modeling and what type of Study (e.g., steady-state, time-dependent, frequency-domain, or eigenfrequency analysis) you will carry out, the Wizard automatically creates one node of each type and shows you their contents. 18

19 It is also possible to add more Component and Study nodes as you develop the model. A model can contain multiple Component and Study nodes and it would be confusing if they all had the same name. Therefore, these types of nodes can be renamed to be descriptive of their individual purposes. If a model has multiple Component nodes, they can be coupled to form a more sophisticated sequence of simulation steps. Note that each Study node may carry out a different type of computation, so each one has a separate Compute button. Keyboard Shortcuts Keyboard Shortcuts To be more specific, suppose that you build a model that simulates a coil assembly that is made up of two parts, a coil and a coil housing. You can create two Component nodes, one that models the coil and the other the coil housing. You can then rename each of the nodes with the name of the object. Similarly, you can also create two Study nodes, the first simulating the stationary or steady-state behavior of the assembly, and the second simulating the frequency response. You can rename these two nodes to be Stationary and Frequency Domain. When the model is complete, save it to a file named Coil Assembly.mph. At that point, the model tree in the Model Builder looks like the figure below. In this figure, the root node is named Coil Assembly.mph, indicating the file in which the model is saved. The Global Definitions node and the Results node each have their default name. Additionally, there are two Component nodes and two Study nodes with the names chosen in the previous paragraph. 19

20 PARAMETERS, VARIABLES, AND SCOPE Parameters Parameters are user-defined constant scalars that are usable throughout the model. That is to say, they are global in nature. Important uses are: Parameterizing geometric dimensions. Specifying mesh element sizes. Defining parametric sweeps (that is, simulations that are repeated for a variety of different values of a parameter such as a frequency or a load). A parameter expression can contain numbers, parameters, built-in constants, built-in functions with parameter expressions as arguments, and unary and binary operators. For a list of available operators, see Appendix C Language Elements and Reserved Names on page 155. Because these expressions are evaluated before a simulation begins, parameters may not depend on the time variable t. Likewise, they may not depend on spatial variables like x, y, or z, nor on the dependent variables that your equations are solving for. It is important to know that the names of parameters are case sensitive. You define Parameters in the model tree under Global Definitions. Variables Variables can be defined either in the Global Definitions node or in the Definitions subnode of any Component node. Naturally, the choice of where to define the 20

21 variable depends on whether you want it to be global (that is, usable throughout the model tree) or locally defined within a single Component node. Like a Parameter Expression, a Variable Expression may contain numbers, parameters, built-in constants, and unary and binary operators. However, it may also contain Variables like t, x, y, or z; functions with Variable Expressions as arguments; and dependent variables that you are solving for in addition to their space and time derivatives. Variables Used in Applications Model parameters and variables can be used in applications. For example, you can let the user of an application change the value of a parameter. In addition, variables to be used in applications can be defined in the Application Builder under the Declarations node. Scope The scope of a Parameter or Variable is a statement about where it may be used in an expression. All Parameters are defined in the Global Definitions node of the model tree. This means that they are global in scope and can be used throughout the model tree. A Variable may also be defined in the Global Definitions node and have global scope, but they are subject to other limitations. For example, Variables may not be used in Geometry, Mesh, or Study nodes (with the one exception that a Variable may be used in an expression that determines when the simulation should stop). A Variable that is defined, instead, in the Definitions subnode of a Component node has local scope and is intended for use in that particular Component (but, again, not in Geometry or Mesh nodes). They may be used, for example, to specify material properties in the Materials subnode of a Component or to specify boundary conditions or interactions. It is sometimes valuable to limit the scope of the variable to only a certain part of the geometry, such as certain boundaries. For that purpose, provisions are available in the settings for a Variable to select whether to apply the definition either to the entire geometry of the Component, or only to certain Domains, Boundaries, Edges, or Points. 21

22 The figure at left shows the definition of two Variables, q_pin and R, for which the scope is limited to just two boundaries identified by numbers 15 and 19. Such Selections can be named and then referenced elsewhere in a model, such as when defining material properties or boundary conditions that will use the Variable. To give a name to the Selection, click the Create Selection button ( ) to the right of the Selection list. Although Variables defined in the Definitions subnode of a Component node are intended to have local scope, they can still be accessed outside of the Component node in the model tree by being sufficiently specific about their identity. This is done by using a dot-notation where the Variable name is preceded by the name of the Component node in which it is defined and they are joined by a dot. In other words, if a Variable named foo is defined in a Component node named MyModel, then this variable may be accessed outside of the Component node by using MyModel.foo. This can be useful, for example, when you want to use the variable to make plots in the Results node. Variables defined under the Declarations node in the Application Builder are available globally in form objects and methods but cannot be used in the Model Builder. Built-In Constants, Variables, and Functions COMSOL Multiphysics comes with many built-in constants, variables, and functions. They have reserved names that cannot be redefined by the user. If you use a reserved name for a user-defined variable, parameter, or function, the text you enter will turn orange (a warning) or red (an error) and you will get a tooltip message if you select the text string. Some important examples are: Mathematical constants such as pi ( ) or the imaginary unit i or j 22

23 Physical constants such as g_const (acceleration of gravity), c_const (speed of light), or R_const (universal gas constant) The time variable, t First-and-second-order derivatives of the Dependent variables (the solution) whose names are derived from the spatial coordinate names and Dependent variable names (which are user-defined variables) Mathematical functions such as cos, sin, exp, log, log10, and sqrt See Appendix C Language Elements and Reserved Names on page 155 for more information..the following spread shows an example of a customized desktop with additional windows. 23

24 SETTINGS WINDOW RIBBON QUICK ACCESS TOOLBAR MODEL BUILDER WINDOW MODEL TREE PLOT WINDOW The Plot window is used to visualize Results quantities, probes, and convergence plots. Several Plot windows can be used to show multiple results simultaneously. 24

25 GRAPHICS WINDOW DYNAMIC HELP Continuously updated with online access to the Knowledge Base and Application Gallery. The Help window enables easy browsing with extended search functionality. INFORMATION WINDOWS PROGRESS BAR WITH CANCEL BUTTON 25

26 The Application Libraries The Application Libraries are collections of MPH files containing tutorial models and runnable applications with accompanying documentation. Tutorial models have documentation that includes the theoretical background and step-by-step instructions. Runnable applications have instructions on how to use the application. You can readily edit all tutorial models and applications to make them your own. Each physics-based add-on module comes with its own application library with examples specific to its applications and physics area. You can use the step-by-step instructions and the MPH files as a template for your own modeling. To open the Application Libraries window, on the Home toolbar, Windows menu select Application Libraries or select File>Application Libraries and then search by application name or browse under a module folder name. Click Open Application, Run Application, or Open PDF Document. Alternatively, select File>Help>Documentation in COMSOL Multiphysics to search by application name or browse by module. Note that the Run Application option is only available for MPH files that are runnable applications. 26

27 The MPH files in the COMSOL Application Library can have two formats Full MPH files or Compact MPH files: Full MPH files, including all meshes and solutions. In the Application Libraries window, these appear with the icon. If the MPH file s size exceeds 25MB, a tip with the text Large file and the file size appears when you position the cursor at the model s node in the Application Libraries tree. Compact MPH files with all settings for the model but without built meshes and solution data to save space on the DVD (a few MPH files have no solutions for other reasons). You can open these to study the settings and to mesh and re-solve the applications. It is also possible to download the full versions with meshes and solutions of most of these when you update your Application Library. These appear in the Application Libraries window with the icon. If you position the cursor at a compact file in the Application Libraries window, a No solutions stored message appears. If a full MPH file is available for download, the corresponding node s context menu includes a Download File with Solutions option. The Application Libraries are updated on a regular basis by COMSOL. To check all available updates, select Update COMSOL Application Library from the File>Help menu (Windows users) or from the Help menu (OS X and Linux users). This connects you to the COMSOL website where you can access new applications and the latest updates. 27

28 Workflow and Sequence of Operations In the Model Builder window, every step of the modeling process, from defining global variables to the final report of results, is displayed in the model tree. From top to bottom, the model tree defines an orderly sequence of operations. In the following branches of the model tree, the node order makes a difference and you can change the sequence of operations by moving the subnodes up or down the model tree: Geometry Materials Physics 28

29 Mesh Study Plot Groups In the Component Definitions branch of the tree, the ordering of the following node types also makes a difference: Perfectly Matched Layer Infinite Elements Nodes may be reordered by these methods: Drag-and-drop Right-clicking the node and selecting Move Up or Move Down Pressing Ctrl + up-arrow or Ctrl + down-arrow In other branches, the ordering of nodes is not significant with respect to the sequence of operations, but some nodes can be reordered for readability. Child nodes to Global Definitions is one such example. You can view the sequence of operations presented as program code statements by saving the model as a model file for MATLAB or as a model file for Java after having selected Compact History in the File menu. Note that the model history keeps a complete record of the changes you make to a model as you build it. As such, it includes all of your corrections including changes to parameters and boundary conditions and modifications of solver methods. Compacting this history removes all of the overridden changes and leaves a clean copy of the most recent form of the model steps. You can also use the Record a New Method option to view and edit program code statements in the Method editor of the Application Builder. As you work with the COMSOL Desktop interface and the Model Builder, you will grow to appreciate the organized and streamlined approach. But any description of a user interface is inadequate until you try it for yourself. So, in the next chapters, you are invited to work through two examples to familiarize yourself with the software. 29

30 Example 1: Structural Analysis of a Wrench This simple example requires none of the add-on products to COMSOL Multiphysics. For more fully-featured structural mechanics models, see the Structural Mechanics Module application library. At some point in your life, it is likely that you have tightened a bolt using a wrench. This exercise takes you through a structural mechanics model that analyzes this basic task from the perspective of the structural integrity of the wrench subjected to a worst-case loading. The wrench is, of course, made from steel, a ductile material. If the applied torque is too high, the tool will be permanently deformed due to the steel s elastoplastic behavior when pushed beyond its yield stress level. To analyze whether the wrench handle is appropriately dimensioned, you will check if the mechanical stress level is within the yield stress limit. This tutorial gives a quick introduction to the COMSOL workflow. It starts with opening the Model Wizard and adding a physics option for solid mechanics. Then a geometry is imported and steel is selected as the material. You then explore the other key steps in creating a model by defining a parameter and boundary condition for the load, selecting geometric entities in the Graphics window, defining the Mesh and Study, and finally examining the results numerically and through visualization. If you prefer to practice with a more advanced model, read this section to familiarize yourself with some of the key features, and then go to the tutorial Example 2: The Busbar A Multiphysics Model on page

31 Model Wizard 1 To start the software, double-click the COMSOL icon on the desktop, which will take you to the New window with two options for creating a new model: Model Wizard or Blank Model. If you select Blank Model, you can right-click the root node in the model tree to manually add a Component and a Study. For this tutorial, click the Model Wizard button. If COMSOL is already open, you can start the Model Wizard by selecting New from the File menu. Choose the Model Wizard. The Model Wizard will guide you through the first steps of setting up a model. The next window lets you select the dimension of the modeling space. 2 In the Select Space Dimension window, select 3D. 3 In Select Physics, select Structural Mechanics > Solid Mechanics (solid). Click Add. Without add-on modules, Solid Mechanics is the only physics interface available in the Structural Mechanics folder. In the picture to the right, the Structural Mechanics folder is shown as it appears when all add-on modules are available. Click Study to continue. 31

32 4 Click Stationary under Preset Studies. Click Done once you have finished. Preset Studies have solver and equation settings adapted to the selected physics; in this example, Solid Mechanics. A Stationary study is used in this case there are no time-varying loads or material properties. Any selection from the Custom Studies branch requires manual settings. Geometry This tutorial uses a geometry that was previously created and stored in the COMSOL native CAD format,.mphbin. To learn how to build your own geometry, see Appendix A Building a Geometry on page 136. File Locations The location of the application library that contains the file used in this exercise varies based on the software installation and operating system. In Windows, the file path will be similar to: C:\Program Files\COMSOL\COMSOL52\Multiphysics\applications. 32

33 1 In the Model Builder window, under Component 1, right-click Geometry 1 and select Import. As an alternative, you can use the ribbon and click Import from the Geometry tab. 2 In the Settings window for Import, from the Geometry import list, select COMSOL Multiphysics file. 3 Click Browse and locate the file wrench.mphbin in the application library folder of the COMSOL installation folder. Its default location in Windows is C:\Program Files\COMSOL\COMSOL52\Multiphysics\applications\COMSOL_Multiphysics\ Structural_Mechanics\wrench.mphbin Double-click to add or click Open. 33

34 4 Click Import to display the geometry in the Graphics window. Rotate: Click and drag Pan: Right-click and drag 5 Click the wrench geometry in the Graphics window and then experiment with moving it around. As you point to or click the geometry, it changes color. Click the Zoom In, Zoom Out, Go to Default 3D View, Zoom Extents, and Transparency buttons on the Graphics window toolbar to see what happens to the geometry: - To rotate, click and drag anywhere in the Graphics window. - To move, right-click and drag. - To zoom in and out, click the mouse scroll wheel, continue holding it, and drag. - To get back to the original position, click the Go to Default 3D View button on the toolbar. Also see Appendix B Keyboard and Mouse Shortcuts on page 151 for additional information. The imported model has two parts, or domains, corresponding to the bolt and the wrench. In this exercise, the focus will be on analyzing the stress in the wrench. 34

35 Materials The Materials node stores the material properties for all physics and all domains in a Component node. Use the same generic steel material for both the bolt and tool. Here is how to choose it in COMSOL. 1 Open the Add Materials window. You can open the Add Materials window in either of these two ways: - Right-click Component 1>Materials in the Model Builder and select Add Material - From the ribbon, select the Home tab and then click Add Material. 2 In the Add Material window, click to expand the Built-In directory. Scroll down to find Structural steel, right-click, and select Add to Component 1. 3 Examine the Material Contents section in the Settings window for Material to see the properties that are available. Properties with green check marks are used by the physics in the simulation. 4 Close the Add Material window. Also see the busbar tutorial sections Materials on page 61 and Customizing Materials on page 98 to learn more about working with materials. 35

36 Global Definitions You will now define a global parameter specifying the load applied to the wrench. Parameters 1 In the Model Builder, right-click Global Definitions and choose Parameters. 2 Go to the Settings window for Parameters. Under Parameters in the Parameters table or in the fields below the table, enter these settings: - In the Name column or field, enter F. - In the Expression column or field, enter 150[N]. The square-bracket notation is used to associate a physical unit to a numerical value, in this case the unit of force in Newtons. The Value column is automatically updated based on the expression entered once you leave the field or press Return. - In the Description column or field, enter Applied force. If you have a Parameters table with more than one entry, you can sort the table with respect to a particular column by clicking on the corresponding header. The sections Global Definitions on page 57 and Parameters, Functions, Variables and Couplings on page 94 show you more about working with parameters. 36

37 So far you have added the physics and study, imported a geometry, added the material, and defined one parameter. The Model Builder node sequence should now match the figure to the right. The default feature nodes under Solid Mechanics are indicated by a D in the upper-left corner of the node icon. The default nodes for Solid Mechanics are: a Linear Elastic Material model, Free boundary conditions that allow all boundaries to move freely without a constraint or load, and Initial Values for specifying initial displacement and velocity values for a nonlinear or transient analysis (not applicable in this case). At any time, you can save your model and then open it later in exactly the state in which it was saved. 3 From the File Menu, select File > Save As. Browse to a folder where you have write permissions, and save the file as wrench.mph. 37

38 Domain Physics and Boundary Conditions With the geometry and materials defined, you are now ready to set the boundary conditions. 1 In the Model Builder, right-click Solid Mechanics (solid) and select Fixed Constraint. This boundary condition constrains the displacement of each point on a boundary surface to be zero in all directions. You can also use the ribbon and select, from the Physics tab, Boundaries > Fixed Constraint. 2 In the Graphics window, rotate the geometry by clicking anywhere in the window and then dragging the wrench into the position shown. Click on the exposed front surface of the partially modeled bolt. The boundary turns blue indicating that it has been selected. The Boundary number in the Selection list should be Click the Go to Default 3D View button on the Graphics toolbar to restore the geometry to the default view. 38

39 4 In the Model Builder, right-click Solid Mechanics (solid) and select Boundary Load. A Boundary Load node is added to the Model Builder sequence. 5 In the Graphics window, click the Zoom Box button on the toolbar and drag the mouse to select the square region shown in the figure to the right. Release the mouse button to zoom in on the selected region. 6 Select the top socket face (Boundary 111) by clicking the boundary to highlight it in blue and add it to the Selection list. 39

40 7 In the Settings window for Boundary Load, under Force, select Total force as the Load type and enter -F in the text field for the z component. The negative sign indicates the negative z direction (downward). With these settings, the load of 150 N will be distributed uniformly across the selected surface. Note that to simplify the modeling process, the mechanical contact between the bolt and the wrench is approximated with a material interface boundary condition. Such an internal boundary condition is automatically defined by COMSOL and guarantees continuity in normal stress and displacement across a material interface. A more detailed analysis including mechanical contact can be done with the Structural Mechanics Module. Mesh The mesh settings determine the resolution of the finite element mesh used to discretize the model. The finite element method divides the model into small elements of geometrically simple shapes, in this case tetrahedrons. In each tetrahedron, a set of polynomial functions is used to approximate the structural displacement field how much the object deforms in each of the three coordinate directions. In this example, because the geometry contains small edges and faces, you will define a slightly finer mesh than the default setting suggests. This will better resolve the variations of the stress field and give a more accurate result. Refining the mesh size to improve computational accuracy always involves some sacrifice in speed and typically requires increased memory usage. 1 In the Model Builder, under Component 1 click Mesh 1. In the Settings window for Mesh, under Mesh Settings, select Fine from the Element size list. 2 Click the Build All button in the Settings window or on the Mesh toolbar. 40

41 3 After a few seconds the mesh is displayed in the Graphics window. Rotate the wrench to take a look at the element size distribution. Study In the beginning of setting up the model you selected a Stationary study, which implies that COMSOL will use a stationary solver. For this to be applicable, the assumption is that the load, deformation, and stress do not vary in time. The default solver settings will be good for this simulation if your computer has more than 2 GB of in-core memory (RAM). If you should run out of memory, the instructions below show solver settings that make the solver run a bit slower but use up less memory. To start the solver: 41

42 1 Right-click Study 1 and select Compute (or press F8). If your computer s memory is below 2 GB you may at this point get an error message Out of Memory During LU Factorization. LU factorization is one of the numerical methods used by COMSOL for solving the large sparse matrix equation system generated by the finite element method. You can easily solve this example model on a memory-limited machine by allowing the solver to use the hard drive instead of performing all of the computation using RAM. The steps below show how to do this. If your computer has more than 2 GB of RAM you can skip to the end of this section (after step 5 below). 1 If you did not already start the computation, you can access the solver settings from the Study node. In the Model Builder, right-click Study 1 and choose Show Default Solver. 2 Under Study 1>Solver Configurations, expand the Solution 1 node. 3 Expand the Stationary Solver 1 node and click Direct. A Direct solver is a fast and very robust type of solver that requires little or no manual tuning in order to solve a wide range of physics problems. The drawback is that it may require large amounts of RAM. 42

43 4 In the Settings window for Direct, in the General section, select the Out-of-core check box. Change the In-core memory method to Manual. Leave the default In-core memory (MB) setting of 512 MB. This setting ensures that if your computer runs low on RAM during computation, the solver will start using the hard drive as a complement to RAM. Allowing the solver to use the hard drive instead of just RAM will slow the computation down somewhat. 5 Right-click Study 1 and select Compute (or press F8). After a few seconds of computation time, the default plot is displayed in the Graphics window. You can find other useful information about the computation in the Messages and Log windows; click the Messages and Log tabs under the Graphics window to see the kind of information available to you. The Messages window can also be opened from the Windows drop-down list in the Home tab of the ribbon. Displaying Results The von Mises stress is displayed in the Graphics window in a default Surface plot with the displacement visualized using a Deformation subnode. Change the default unit (N/m 2 ) to the more suitable MPa as shown in the following steps. 43

44 1 In the Model Builder, expand the Results>Stress (solid) node, then click Surface 1. 2 In the Settings window under Expression, from the Unit list select MPa (or type MPa in the field). To study the stress more accurately, expand the Quality section. From the Recover list select Within domains. This setting will recover information about the stress level from a collection of elements rather than from each element individually. It is not active by default since it makes visualizations slower. The Within domain setting treats each domain separately, and the stress recovery will not cross material interfaces. 44

45 3 Click the Plot button on the toolbar of the Settings window for the Surface plot and then click the Go to Default 3D View button on the Graphics window toolbar. The plot is regenerated with the updated unit and using the Within domain recovery setting. The von Mises stress distribution is shown in the bolt and wrench under an applied vertical load. For a typical steel used for tools like a wrench, the yield stress is about 600 MPa, which means that we are getting close to plastic deformation for our 150 N load (which corresponds to about 34 pounds force). You may also be interested in a safety margin of, say, a factor of three. To quickly assess which parts of the wrench are at risk of plastic deformation, you can plot an inequality expression such as solid.mises>200[mpa]. 1 Right-click the Results node and add a 3D Plot Group. 45

46 2 Right-click the 3D Plot Group 2 node and select Surface. 3 In the Settings window for Surface, click the Replace Expression button and select Model>Component1>Solid Mechanics>Stress>solid.mises-von Mises stress by double-clicking. When you know the variable name beforehand, you can also directly enter solid.mises in the Expression field. Now edit this expression to: solid.mises>200[mpa]. This is a boolean expression that evaluates to either 1, for true, or 0, for false. In areas where the expression evaluates to 1, the safety margin is exceeded. Here, you also use the Recover feature described earlier. 4 Click the Plot button. 5 In the Model Builder, click 3D Plot Group 2. Press F2 and in the Rename 3D Plot Group dialog box, enter Safety Margin. Click OK. The resulting plot shows that the stress in the bolt is high, but the focus of this exercise is on the wrench. If you wished to comfortably certify the wrench for a 46

47 150 N load with a factor-of-three safety margin, you would need to change the handle design somewhat, such as making it wider. You may have noticed that the manufacturer, for various reasons, has chosen an asymmetric design for the wrench. Because of that, the stress field may be different if the wrench is flipped around. Try now, on your own, to apply the same force in the other direction and visualize the maximum von Mises stress to see if there is any difference. Convergence Analysis To check the accuracy of the computed maximum von Mises stress in the wrench, you can now continue with a mesh convergence analysis. Do that by using a finer mesh and therefore a higher number of degrees of freedom (DOFs). This section illustrates some more in-depth functionality and the steps below could be skipped at a first reading. In order to run the convergence analysis below, a computer with at least 4GB of memory (RAM) is recommended. EVALUATING THE MAXIMUM VON MISES STRESS 1 To study the maximum von Mises stress in the wrench, in the Results section of the model tree, right-click the Derived Values node and select Maximum>Volume Maximum. 47

48 2 In the Settings window for Volume Maximum, under Selection, choose Manual and select the wrench, domain 1, by clicking on the wrench in the Graphics window. We will only consider values in the wrench domain and neglect those in the bolt. 3 In the Expression text field enter the function ppr(solid.mises). The function ppr() corresponds to the Recover setting in the earlier note on page 44 for Surface plots. The Recover setting with the ppr function is used to increase the quality of the stress field results. It uses a polynomial-preserving recovery (ppr) algorithm, which is a higher-order interpolation of the solution on a patch of mesh elements around each mesh vertex. It is not active by default since it makes Results evaluations slower. 4 Under Expression, select or enter MPa as the Unit. 5 In the Settings window for Volume Maximum, click Evaluate to evaluate the maximum stress. The result will be displayed in a Table window and will be approximately 364 MPa. 6 To see where the maximum value is attained, you can use a Max/Min Volume plot. Right-click the Results node and add a 3D Plot Group. 7 Right-click the 3D Plot Group 3 node and select More Plots>Max/Min Volume. 8 In the Settings window for Max/Min Volume, in the Expression text field, enter the function ppr(solid.mises). 9 In the Settings window under Expression, from the Unit list select MPa (or enter MPa in the field). 48